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Index B-spline

In the mathematical subfield of numerical analysis, a B-spline, or basis spline, is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. [1]

42 relations: Basis function, Bézier curve, Box spline, Cauchy distribution, Chebyshev filter, Composite Bézier curve, Computer graphics, Computer-aided design, Computer-aided manufacturing, Continuous function, Curve fitting, De Boor's algorithm, Degree of a polynomial, Divided differences, Domain of a function, Exponential function, Fortran, Homogeneous coordinates, I-spline, Isaac Jacob Schoenberg, Least squares, Linear combination, Loss function, M-spline, Mathematics, Moving average, Normal distribution, Numerical analysis, Numerical differentiation, Overfitting, Penalty method, Piecewise, Polynomial, Savitzky–Golay filter, Smoothness, Spline (mathematics), Spline wavelet, Support (mathematics), T-spline, Tensor product, Terminology, Triangular function.

Basis function

In mathematics, a basis function is an element of a particular basis for a function space.

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Bézier curve

A Bézier curve (pronounced in French) is a parametric curve frequently used in computer graphics and related fields.

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Box spline

In the mathematical fields of numerical analysis and approximation theory, box splines are piecewise polynomial functions of several variables.

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Cauchy distribution

The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution.

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Chebyshev filter

Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple (type I) or stopband ripple (type II) than Butterworth filters.

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Composite Bézier curve

In geometric modelling and in computer graphics, a composite Bézier curve is a piecewise Bézier curve that is at least continuous.

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Computer graphics

Computer graphics are pictures and films created using computers.

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Computer-aided design

Computer-aided design (CAD) is the use of computer systems to aid in the creation, modification, analysis, or optimization of a design.

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Computer-aided manufacturing

Computer-aided manufacturing (CAM) is the use of software to control machine tools and related ones in the manufacturing of workpieces.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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Curve fitting

Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.

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De Boor's algorithm

In the mathematical subfield of numerical analysis de Boor's algorithmC.

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Degree of a polynomial

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

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Divided differences

In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions.

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Domain of a function

In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.

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Exponential function

In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.

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Fortran (formerly FORTRAN, derived from Formula Translation) is a general-purpose, compiled imperative programming language that is especially suited to numeric computation and scientific computing.

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Homogeneous coordinates

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.

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In the mathematical subfield of numerical analysis, an I-spline is a monotone spline function.

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Isaac Jacob Schoenberg

Isaac Jacob Schoenberg (April 21, 1903 – February 21, 1990) was a Romanian-American mathematician, known for his discovery of splines.

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Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.

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Linear combination

In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).

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Loss function

In mathematical optimization, statistics, econometrics, decision theory, machine learning and computational neuroscience, a loss function or cost function is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event.

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In the mathematical subfield of numerical analysis, an M-spline is a non-negative spline function.

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Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Moving average

In statistics, a moving average (rolling average or running average) is a calculation to analyze data points by creating series of averages of different subsets of the full data set.

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Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

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Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

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Numerical differentiation

In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.

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In statistics, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit additional data or predict future observations reliably".

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Penalty method

Penalty methods are a certain class of algorithms for solving constrained optimization problems.

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In mathematics, a piecewise-defined function (also called a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain, a sub-domain.

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In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

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Savitzky–Golay filter

A Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the signal-to-noise ratio without greatly distorting the signal.

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In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.

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Spline (mathematics)

In mathematics, a spline is a function defined piecewise by polynomials.

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Spline wavelet

In the mathematical theory of wavelets, a spline wavelet is a wavelet constructed using a spline function.

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Support (mathematics)

In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero.

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A T-spline surface can be thought of as a NURBS surface for which a row of control points is allowed to terminate without traversing the entire surface.

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Tensor product

In mathematics, the tensor product of two vector spaces and (over the same field) is itself a vector space, together with an operation of bilinear composition, denoted by, from ordered pairs in the Cartesian product into, in a way that generalizes the outer product.

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Terminology is the study of terms and their use.

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Triangular function

A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle.

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B spline, B splines, B-Spline, B-spline surface, B-splines, Basis B-spline, Bspline, P-spline.


[1] https://en.wikipedia.org/wiki/B-spline

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